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Number theory Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

Noah writes down the numbers 1, 2, 4 and 13. He then adds a fifth integer $x$ which then becomes the mean, median or mode of the five numbers. How many possible choices for $x$ are there?

(A) $2$ (B) $3$ (C) $4$ (D) $5$ (E) $6$

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